One of the most basic electrical junctions used in modern devices is the metal-semiconductor junction. In these junctions, a metal (such as aluminum) is brought in contact with a semiconductor (such as silicon). This forms a device (a diode) which can be inherently rectifying; that is, the junction will tend to conduct current in one direction more favorably than in the other direction. In other cases, depending on the materials used, the junction may be ohmic in nature (i.e., the contact may have negligible resistance regardless of the direction of current flow). Grondahl and Geiger first studied the rectifying form of these junctions in 1926, and by 1938 Schottky had developed a theoretical explanation for the rectification that was observed.
Schottky's theory explained the rectifying behavior of a metal-semiconductor contact as depending on a barrier at the surface of contact between the metal and the semiconductor. In this model, the height of the barrier (as measured by the potential necessary for an electron to pass from the metal to the semiconductor) was postulated as the difference between the work function of the metal (the work function is the energy required to free an electron at the Fermi level of the metal, the Fermi level being the highest occupied energy state of the metal at T=0) and the electron affinity of the semiconductor (the electron affinity is the difference between the energy of a free electron and the conduction band edge of the semiconductor). Expressed mathematically:φB=φM−χS  [1]where ΦB is the barrier height, ΦM is the work function of the metal and χS is the electron affinity of the semiconductor.
Not surprisingly, many attempts were made to verify this theory experimentally. If the theory is correct, one should be able to observe direct variations in barrier heights for metals of different work functions when put in contact with a common semiconductor. What is observed, however, is not direct scaling, but instead only a much weaker variation of barrier height with work function than implied by the model.
Bardeen sought to explain this difference between theoretical prediction and experimental observation by introducing the concept that surface states of the semiconductor play a role in determining the barrier height. Surface states are energy states (within the bandgap between the valence and conduction bands) at the edge of the semiconductor crystal that arise from incomplete covalent bonds, impurities, and other effects of crystal termination. FIG. 1 shows a cross-section of an un-passivated silicon surface labeled 100. The particular silicon surface shown is an Si(100)2×1 surface. As shown, the silicon atoms at the surface, such as atom 110, are not fully coordinated and contain un-satisfied dangling bonds, such as dangling bond 120. These dangling bonds may be responsible for surface states that trap electrical charges.
Bardeen's model assumes that surface states are sufficient to pin the Fermi level in the semiconductor at a point between the valence and conduction bands. If true, the barrier height at a metal-semiconductor junction should be independent of the metal's work function. This condition is rarely observed experimentally, however, and so Bardeen's model (like Schottky's) is best considered as a limiting case.
For many years, the cause underlying the Fermi level pinning of the semiconductor at a metal-semiconductor junction remained unexplained. Indeed, to this day no one explanation satisfies all experimental observations regarding such junctions. Nevertheless, in 1984, Tersoff proposed a model that goes a long way towards explaining the physics of such junctions. See J. Tersoff, “Schottky Barrier Heights and the Continuum of Gap States,” Phys. Rev. Lett. 52 (6), Feb. 6, 1984.
Tersoff's model (which is built on work by Heine and Flores & Tejedor, and see also Louie, Chelikowsky, and Cohen, “Ionicity and the theory of Schottky barriers,” Phys. Rev. B 15, 2154 (1977)) proposes that the Fermi level of a semiconductor at a metal-semiconductor interface is pinned near an effective “gap center”, which is related to the bulk semiconductor energy band structure. The pinning is due to so-called metal induced gap states (MIGS), which are energy states in the bandgap of the semiconductor that become populated due to the proximity of the metal. That is, the wave functions of the electrons in the metal do not terminate abruptly at the surface of the metal, but rather decay in proportion to the distance from that surface (i.e., extending inside the semiconductor). To maintain the sum rule on the density of states in the semiconductor, electrons near the surface occupy energy states in the gap derived from the valence band such that the density of states in the valence band is reduced. To maintain charge neutrality, the highest occupied state (which defines the Fermi level of the semiconductor) will then lie at the crossover point from states derived from the valence band to those derived from the conduction band. This crossover occurs at the branch point of the band structure. Although calculations of barrier heights based on Tersoff's model do not satisfy all experimentally observed barrier heights for all metal-semiconductor junctions, there is generally good agreement for a number of such junctions.
One final source of surface effects on diode characteristics is inhomogeneity. That is, if factors affecting the barrier height (e.g., density of surface states) vary across the plane of the junction, the resulting properties of the junction are found not to be a linear combination of the properties of the different regions. In summary then, a classic metal-semiconductor junction is characterized by a Schottky barrier, the properties of which (e.g., barrier height) depend on surface states, MIGS and inhomogeneities.
The importance of the barrier height at a metal-semiconductor interface is that it determines the electrical properties of the junction. Thus, if one were able to control or adjust the barrier height of a metal-semiconductor junction, one could produce electrical devices of desired characteristics. Such barrier height tuning may become even more important as device sizes shrink even further. Before one can tune the barrier height, however, one must depin the Fermi level of the semiconductor. As discussed in detail below, the present inventors have achieved this goal in a device that still permits substantial current flow between the metal and the semiconductor.